I do not have a very advanced understanding of binding energy and atomic mass but in my classes, I have learned that the atomic mass is equal to the sum of the number of protons and the number of neutrons. But I know this to not be the case every time because during fusion energy is emitted due to the mass of the product (say, Helium-4) being lighter than the nuclei that you started with (say, 2 protium nuclei). In a book (The Universe in your hand), I read that the difference in mass from which the energy is emitted (due to E=mc^2) is actually from the mass of the mesons (two quarks?) and gluons that carry the strong force between the quarks and between protons and neutrons. According to the book, when fusion occurs the number of gluons and mesons required to hold the atom together is less (the binding energy?), and therefore the total mass decreases.

Now my question is, why does this fusion cause a decrease in mass? For example, why does a hydrogen-2 nucleus have less binding energy, i.e. have fewer mesons and gluons, than two hydrogen-1 nuclei? The hydrogen-1 nuclei should not require any mesons since they only consist of a proton, don't they? If someone could explain this I would be very grateful.

Please inform me of potential errors. :)


Binding Energy is considered negative because it's the energy needed to separate the constituent parts.

Suppose you have a simple Hydrogen atom, just a proton and an electron. You need 13.6eV to separate the proton and electron an infinite distance away from each other.

So the energy of the atom in the ground state is $m_pc^2+m_ec^2+BE$ where BE=-13.6 eV. Note the minus sign.

So the energy does roughly increase with the rest mass of the constituent parts because the binding energy is orders of magnitude smaller than the constituent parts.

Now suppose the hydrogen atom has a neutron in addition to the proton. Then we get new terms in the sum of the energy. We have to add $m_nc^2$ for the mass energy of the neutron. But then the neutron is bonded to the proton via the strong force, we have a new Binding Energy term. There's also some angular momentum terms now that might not show up in the individual rest masses or the binding energy.

So we expect a smaller mass-energy for particles bound together because we need to add energy to break them up into constituent parts. The need to add to get to the total rest energy of the parts suggests a deficit, so the binding energy is negative.


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